Peclet criterion

Plug flow is approached at low values of the dispersion coefficient or hi values or Peclet number. A criterion developed by Mears (Chem. Eng. Sci., 26, 1361 [1971]) is that conversion will be within 5 percent of that predicted by phig flow when... 

To treat current distribution in through-holes, Hazlebeck and Talbot [140] formulated a model and established dimensionless criteria for ohmic and convective regimes. The most uniform distribution is obtained in the ohmically limited regime bounded by a numerical criterion based on a Peclet number and a Thiele modulus yT. In the notation of Takahashi and Gross,... 

At this point, it is also important to check the plug-flow assumption as the simple model assumes plug flow for the liquid. For the specified Reynolds number, the Peclet number is found to be 0.59 using the Michell-Furzer correlation (eq. 3.417). The minimum value of Z/d, evaluated using the Mears criterion, is 15.87 (eq. (3.421)), lower than the value used in the experiments, which is about 30. Thus, the operation can be assumed as plug flow. 

Numeric dispersion can be eliminated largely by a high-resolution discretisation. The Grid-Peclet number helps for the definition of the cell size. Pinder and Gray (1977) recommend the Pe to be < 2. The high resolution discretisation, however, leads to extremely long computing times. Additionally the stability of the numeric finite-differences method is influenced by the discretisation of time. The Courant number (Eq. 104) is a criterion, so that the transport of a particle is calculated within at least one time interval per cell. 

It can be seen that the central differencing scheme discussed above is conservative. The coefficients of CDS satisfy the Scarborough criterion. However, for uniform grid (Ae = 0.5), when the Peclet number is higher than 2, the coefficients oe will become negative [Fg > This violates the boundedness requirements and may... 

Plug-flow assumption Using tire Michell and Fmzer conelation (eq. (3.417)), the liquid-phase Peclet value is 0.66 and tire minimum value of Zld, evaluated by using the Meai s criterion (eq. (3.421)) 4.81, which is much lower that the experimental one, which is 100. Then, condition (c) is satisfied. 

If we set Co and in the criterion of equation (i) as the inlet and outlet concentrations of sulfur, the effect of axial dispersion can be evaluated quantitatively. We will employ the correlation of Hochman and Effron [J.M. Hochman and E. Effron, Ind. Eng. Chem. Fundls., 8, 63 (1969)] for Peclet number... 

The reactor was modeled as an axial dispersion unit The most common single criterion for the extent of axial dispersion is the Peclet (Pe) number. A study highlighting the importance of the effect of Pe number and the effect of the extent of axial dispersion on the productivity was included. Sensitivity of the model parameters to possible inaccuracy in the value of Pe number was also studied. The value of Pe number that was used in simulation studies was obtained from empirical correlations presented in the literature [24-26]. 

Like any diagnostic test, the criteria given above must be used with caution. For example, the axial and radial Peclet numbers (2 and 10, respectively, see Sections 4.10.7.2 and 4.10.6.4) used to derive the criteria may deviate for Re < 10 to lower Pe values by factors of up to 5. This would lead to a more restrictive criterion. 

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